Qualitative Analysis of a Three-Species Ratio-Dependent Lotka–Volterra Model with Cautious Effect and Feedback Control

This paper presents a qualitative analysis of a three-species ratio-dependent Lotka–Volterra model that incorporates cautious effect and feedback control. These two mechanisms serve as core regulatory factors in population dynamics, and their integration into the classical framework significantly enhances the biological realism of the model. For the persistence property, we apply the comparison principle of differential equations together with inequality techniques to derive sufficient conditions. For the global attractivity, we construct appropriate Lyapunov functionals and employ Lyapunov stability theory to establish sufficient conditions. A numerical example is finally provided to validate the correctness of the proposed theoretical results. Our findings indicate that the combined action of cautious effect and feedback control can effectively reduce extinction risks and suppress excessive population fluctuations in three-species ratio-dependent systems, thereby offering a quantitative basis for precise ecosystem management.